COGNITIVE SCIENCE 6, 291-330 (1982)
Intensi0nal Concepts in Propositional
Semantic Networks*
A N T H O N Y S. M A I D A
Brown University
STUART C. S H A P I R O
State University of New York at Buffalo
An integrated statement is made concerning the semantic status of nodes in a
propositional semantic network, claiming that such nodes represent only intensions. Within the network, the only reference to extensionality is via a
mechanism to assert that two intensions have the same extension in some
world. This framework is employed in three application problems to illustrate
the nature of its solutions.
The formalism used here utilizes only assertional information and no structural, or definitional, information. This restriction corresponds to many of the
psychologically motivated network models. Some of the psychological implications of network processes called node merging and node splitting ore
discussed. Additionally, it is pointed out that both our networks and the
psychologically based networks are prone to memory confusions about knowing unless augmented by domain-specific inference processes, or by structural information.
INTRODUCTION
In this paper, we discuss a particular kind o f semantic network. It is a representation o f knowledge consisting o f nodes a n d labeled, directed arcs in
which the following conditions hold (cf. Shapiro, 1971): I) each n o d e represents a unique concept; 2) each concept represented in the network is represented by a node; 3) each concept represented in the n e t w o r k is represented
by a unique node (the Uniqueness Principle); 4) arcs represent n o n - c o n c e p *The work presented here was partly supported by the National Science Foundation
under Grant No. MCS78-02274 and MCS80--06314. We appreciate the comments and suggestions of the members of the Graduate Group in Cognitive Science and of the SNePS Research
Group, both of SUNY at Buffalo. We also thank one of the anonymous reviewers for very
extensive comments.
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tual binary relations between nodes; 5) the knowledge represented about
each concept is represented by the structure of the entire network connected
to the node representing the concept. The term propositional semantic network is sometimes used to distinguish those semantic networks in which
every assertion that can be stored or accessed in the network is considered a
concept, and therefore represented by a node, from those networks in which
some such assertions are represented by arcs (most notably set membership
and subset relationships, cf. Hendrix, 1979, p. 54; or statements without
handle nodes, cf. Fahlman, 1979, p. 112). This paper is concerned with
propositional semantic networks so understood. Conceivably, conceptual
dependency networks (cf. Schank, 1975) could be classified as propositional
semantic networks if their syntax were explicated. We are using the term
proposition because propositions are the intensions of sentences. The definition also allows for the use of nodes corresponding to functional individuals.
We will more closely examine the Uniqueness Principle in order to help
understand the semantics of semantic networks. In doing this, we follow the
line of research exemplified by Woods (1975) and Brachman (1977, 1979).
The major point will be that nodes represent only intensions and not extensions, e.g., individual concepts rather than referents, and propositions
rather than truth values. Insisting that semantic networks be allowed to
represent only intensions suggests promising approaches to several knowledge representation problems which often lead to confusion. One of our
goals is to devise a representation which is rich enough to maintain the subtle
distinctions related to referential opacity and extensional equivalence. The
purpose of the representation is to provide a substrate by which processes
(e.g., programs, production rules, and inference rules) can operate.
The first problem we treat concerns indirect reference, originally
raised by Frege (1892) and recently discussed by McCarthy (1979). McCarthy
has put the problem into the following form:
the meaning of the phrase "Mike's telephone number" in the sentence
"'Pat knows Mike's telephone number" is the concept of Mike's telephone number, whereas its meaning in the sentence "'Pat dialled Mike's
telephone number" is the number itself. Thus if we also have "Mary's
telephone number=Mike's telephone number," then "Pat dialled
Mary's telephone number" follows, but "'Pat knows Mary's telephone
number" does not. (p. 129-130, italics in original)
Knowing is said to create an opaque context in its complement position and
dialling is said to create a transparent context. The Uniqueness Principle
suggests a solution strategy for this problem. We treat the concept of Mike's
phone number and the concept of the number itself as distinct intensions,
and thereby create a representional substrate with sufficient resolution to
control inference processes which differentially apply in opaque and transparent contexts.
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The second problem we treat is that of representing the concept of the
truth value of a proposition. Since it is meaningful to talk about the truth
value of a proposition independently of whether we know the proposition is
true or false, we should have the ability to explicitly represent the truth
value if we need to. For example, any semantic representation of the sentence " J o h n knows whether he is taller than Bill" seems to explicitly reference the proposition underlying the sentence " J o h n is taller than Bill." This
seems clear after examining the paraphrase " J o h n knows the truth value of
the proposition John is taller than Bill."
Finally, we show how questions may be represented in propositional
semantic networks. By this we mean how to represent the proposition that
someone requested certain information of someone else. Such a proposition
is contained in the sentence " I got mad because John asked me whether I
was a boy or a girl."
HISTORY OF THE PROBLEMS
In this section, we briefly review the histories of three problems in knowledge representation for which we propose new solutions later in the paper.
The main thrust of this paper is an investigation of the semantics of one
kind of semantic network. That the theory leads to nice solution strategies
for the three problems should be taken as a further explication of and support for the theory.
We can trace the emergence in artificial intelligence (AI) of the first
problem to a paper by McCarthy and Hayes (1969) and it surfaced in its
present form in later papers by McCarthy (1977, 1979). A well known philosophical solution to this problem, offered by Quine (1956) is to treat knows
as an operator which creates an opaque context and to disallow substitution
of equals by equals in an opaque context. Another approach has been
adopted by Moore (1977, 1980). He encodes Hintikka's (1971) modal logic
of knowledge within first-order logic and then builds an inference engine
for that logic. An approach also using first-order logic is taken by McCarthy
(1979) and Creary (1979). These researchers propose to view a concept as an
object of discourse within the logic. They have one term which denotes
Mike's phone number and another which denotes the concept of that phone
number. This enables them to bypass the problem of replacement of equals
by equals because the concept of Mike's phone number and the number
itself are different entities. We differ from McCarthy in that we use one
node to denote the concept of Mike's phone number and another node to
denote the concept of the number itself.
One attempt to represent information about knowledge and belief in a
semantic network was offered by Cohen (1978), but it is unclear how his
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treatment would relate to the issues raised in this paper. His primary goal
was to show how a speaker's beliefs about a heater's beliefs influences the
speaker's planning of speech acts. Anderson (1977, 1978) has sketched a
semantic network based procedure for processing referring expressions.
Anderson's approach involves creating two distinct nodes in the network
for the two concepts (i.e., the concept of Mike's phone number and its
referent), and perhaps was inspired by Woods' (1975) important paper. He
does not work out the details of representing belief, as they are not his
primary goal. He does some interesting reaction time experiments which
partly test the psychological reality of the Anderson-Woods proposal and
these will be discussed later in the paper.
The solution we propose is in the spirit of Anderson but is more thoroughly articulated in the following ways: 1) we specify exactly how the
nodes are related and which features of the representation trigger which
kinds of inference processes; 2) we provide the solution with well articulated
philosophical underpinnings; 3) we point out that these same philosophical
assumptions provide an identical solution to some, at first glance, unrelated
problems; 4) Anderson's experiments used stimulus materials which involved
only transparent contexts. We suggest that the experimental results will not
generalize to opaque contexts; and, 5) We point out that Anderson's model,
if it is straight-forwardly extended, predicts some counter intuitive memory
confusions.
The second problem, of representing the notion of truth value, has
not received much attention in the AI literature, probably because the problem domains which have been attacked by AI researchers have allowed
domain specific solutions. We feel the problem deserves more attention for
two reasons. First, the notion of truth value in general and the notion of the
truth value of a specific proposition in particular can be objects of thought
themselves. Since propositional semantic networks are supposed to be knowledge representations in which every concept (object of thought) is represented by a node, the notion of truth value should also be so represented.
Second, having decided that truth values of propositions might be represented by nodes in a semantic network, we quickly find where such nodes
can be useful. For example, utterance (1)
(1) John knows whether he is taller than Bill.
can be taken as an assertion that mentions the truth value of the proposition
that John is taller than Bill without taking a position on whether it is true or
false. Thus, in order to represent (1) as a proposition about a truth value,
we need to be able to represent a truth value independently of the specific
value (true or false) it happens to be. An alternative solution used by Allen
(1979) and Cohen and Perrault (1979) involves specifying the meaning of
"knowing whether" as a disjunction of correct beliefs. For instance, the disjunction (2) could serve as the representation for "John knows whether P . "
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
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(2) (P & John believes P) or
(not P & John believes not P)
We claim that this representation uses the intensions P, John believes P, not
P, and John believes not P, but it does not use the intension of the truth
value o f P, which is, we believe, the intension o f "whether P . "
A simpler example which we shall use throughout this paper is shown
in (3) with its disjunctive reading in (4).
(3) John holds an opinion about whether he is taller than Bill.
(4) John believes he is taller than Bill or John believes he is not taller
than Bill.
This disjunctive solution does not generalize to some embedding verbs such
as " w o n d e r , " which is shown as sentence (5).
(5) John wondered whether P.
Perhaps (5) could be paraphrased as (6a) and thence, via the disjunctive
reading of " k n o w s whether" as (6b). We feel, however, that a better paraphrase is (6c), which mentions the concept o f a truth value explicitly.
(6a) John wanted to know whether P.
(6b) John wanted to know P or to know not P.
(6c) John was curious about the truth value of P.
Our only claims are that a node for the concept o f a truth value should
explicitly exist in the network and is useful for certain representation tasks.
We agree that (3) and (4) are logically equivalent and this can be captured by
inference rules o f some kind. However, logical equivalence is not the same
as intensional identity.
The last of the three problems we discuss, that of representing questions, acquires salience because of our position that propositional semantic
networks represent only intensions and the combined facts that: 1) intensions are meant to correspond to individual concepts or propositions, and 2)
questions are neither individual concepts nor propositions. Other representational schemes can trivially represent questions by tagging the symbol
structure which describes the content of the question as being a question
and not an assertion. For instance, Schank (1975) represents yes-no questions in conceptual dependency diagrams by indicating that the mode o f the
diagram is a question, rather than an assertion. Wh-questions are indicated
by placing the symbol " * ? * " in the question slot. That is, the question
" W h e r e is the salt?" would be represented as something like (LOC SALT
*?*). A propositional network would interpret the notation (LOC SALT *?*)
as a proposition stating that the salt is at the question mark, or a proposition involving a free variable.
It happily turns out that by viewing yes-no questions as enquiries
about truth values we can immediately represent them. Later in the paper,
we attempt to generalize this solution to wh-questions as well.
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THE THEORETICAL FRAMEWORK
What Does a Semantic Network Model?
The first issue we must be clear about is what we intend a semantic network
to model. We first exclude two possibilities.
One possibility is the real world. This would require nodes to represent objects in the world (as opposed to individual concepts) and facts about
such objects (as opposed to propositions). Although some people might be
interested in semantic networks as models of the world, we are not.
A second possibility is that a semantic network models a corpus of
natural language text, or perhaps that a semantic network is a data structure
in which a text is stored and from which pieces of the text can be retrieved
easily. In this case, nodes of the network would represent words, lexemes,
morphemes, strings, phrases, clauses, sentences, and so forth. In Woods
(1975), for example, it is argued that the semantic network representation of
"The dog that had rabies bit the m a n " must distinguish between the proposition of the main clause, "The dog bit the m a n " and the proposition of the
subordinate clause, "The dog had rabies." Woods proposed this for semantic reasons (p. 62). Had he made the proposal for purely syntactic reasons,
then he would have been representing sentences as opposed to meanings.
Although we feel that semantic networks can be used to model natural language text (cf. Shapiro & Neal, 1982), this is not the use with which we are
concerned in this paper.
A third possibility, and the one that we are concerned with, is that a
semantic network models the belief structure of a thinking, reasoning, language using being (e.g., a human). In this case, nodes represent the concepts
and beliefs such a being would have. The point is that these concepts are intensions rather than extensions.
This is not, perhaps, the majority view of researchers in "knowledge
representation." In their survey of knowledge representation research,
Brachman and Smith (1980) asked researchers, "between what two things
do you envisage the 'representation' relationship?" (p. 68). They report,
"The one interesting thing to be said in summary, it seems, is that the
phrase which we use as a commonplace label of our endeavor--'the representation of knowledge'--is perhaps surprisingly not taken in a particularly
literal sense...what was considered to be 'represented', typically, were
various kind of object [sic] in the world" (p. 71). Nevertheless, in answer to
the question, "Would you characterize your inquiry as primarily an investigation into the structure of language, or more as an investigation into the
structure of thought? . . . . The great majority gave their prime allegiance to
the study of thought" (p. 71).
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lntensions
The term "intension" derives from Frege's (1892) term "sense". He was
concerned with the relationship between equality and the meanings of designating expressions in a language. The fact that (7a) is true and (7b) is false
illustrates the problem which concerned Frege.
(7a) Necessarily, the Morning Star is the Morning Star.
(7b) Necessarily, the Morning Star is the Evening Star.
Frege took this as evidence that the designating phrases "the Morning Star"
and "the Evening Star" do not have the same meaning, even though they
denote the same object. If the expressions were equal then (7a) and (7b)
should have identical meaning. Frege used the term "sense" of an expression to intuitively correspond to the meaning of that expression, and he used
the term "reference" to correspond to the denotation of the expression.
Carnap (1947) attempted to formalize Frege's notion of the sense of
an expression as a function from possible states of affairs to denotations.
The function was called an "intension" and the denotation was called an
"extension" (cf. Dowty, Wall, & Peters, 1981, p. 145). The approach was
refined through Kripke's (1963) semantics of necessity and Montague's intensional logic (p. 145).
When we say that nodes of a semantic network represent intensions as
opposed to extensions, we mean sense as opposed to reference. Additionally
for the purposes of this paper, we will not view intensions as functions,
although it might be helpful to do so in the future. When we say that nodes
of a semantic network represent intensions we mean intension as Frege
(1892), McCarthy (1979), and Creary (1979) view intension, as opposed to
Carnap (1947), Kripke (1963), Montague (cf. Dowry, et al.), or Moore
(1980). We take intensions to correspond to concepts, ideas, objects of
thought, or things which can be conceived of.
The Need for lntensional Representations
Woods (1975) appears to have been the first to emphasize that some nodes
of a semantic network should represent intensions. One reason for this is to
enable the cognitive agent being modeled to conceive of things which do not
exist in the actual world such as unicorns and Santa Claus. Although unicorns do not exist, they can be reasoned about. Indeed, the reader can say,
as McCawley (1980) points out, how many horns a two-headed unicorn
would have. Thus, we should be able to describe within a semantic network
any conceivable concept, independently of whether it is realized in the actual
world, and we should also be able to describe whether in fact it is realized.
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Returning to the Morning Star--Evening Star example, Woods (1975)
concluded that, "there must be two mental entities (concepts, nodes, or
whatever) corresponding to the two different intensions, morning star and
evening star. There is then an assertion about these two intensional entities
that they denote one and the same external object (extension)" (p. 50).
Woods continues with the observation that "there must be some nodes in
the network which correspond to descriptions of entities rather than entities
themselves . . . . We have to decide how to tell the two kinds of nodes a p a r t "
(p. 68). Semantic network theorists have not universally agreed with this
position. Schubert, Goebel, and Cercone (1979), for instance say, " W e take
the position that terms (nodes, subnets) already have both extensions and
intensions'" (p. 128, italics in original). Brachman (1977) takes a position on
the other side of Woods, stating, "Semantic networks are representations of
the intensions of natural language designators'" (p. 139, italics in original).
Yet Brachman still allows some extensional information in his networks:
" s o m e of the operations in the network scheme are purely intensional, while
others are n o t " (p. 150).
We want to go even further than Brachman and say that all information in the network is intensional. The only reference to extensions will be
propositions stating that two intensions pick out the same extension in some
world, such as the proposition that the Morning Star is the Evening Star in
the actual world.
The Absence of a Need for Extensional Representation
If, as Woods pointed out, at least some nodes represent intensions, do any
represent extensions? Indeed, should every node be seen as having both an
intension and an extension as Schubert et al. claim and as most philosophers
usually treat designating expressions? Our answer derives from what we
take our networks to model (see above). If a network modeled the real
world, then a node would represent (or denote) an extension, but we take
our networks to model conceptual belief structures.
A node that represents only an intension carries no c o m m i t m e n t that
an object realizing the intension exists in the real world. The standard translation of " T h e present king of France is b a l d " into a logical notation seems
to require asserting the existence of the present king of France.
(EXISTS x) (x is the-present-king-of-France & x is bald).
However, this is because of the normal extensional interpretation of
statements in standard logic. A constant node in a semantic network is like a
Skolem constant derived from a extensionally quantified variable that
asserts only the existence of the intension.
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S T R U C T U R A L I M P L I C A T I O N S OF
I N T E N S I O N A L REPRESENTATION
The Need for Co-referential Propositions
If a semantic network has a node for the intension of the Morning Star and
a different node for the intension of the Evening Star, what should be done
when the assertion is made that the Morning Star is the Evening Star? If the
nodes were merged by transferring all of the arcs from one node to the other
and eliminating the first, then this would eliminate the distinction between
the two concepts and make it impossible to represent the sentence " J o h n
did not know that the Morning Star is the Evening Star" differently from
the sentence " J o h n did not know that the Morning Star is the Morning
S t a r . " The solutiori Woods (1975) proposed is to add a node to the network
representing the proposition underlying the sentence " T h e Morning Star is
co-referential with the Evening Star in the actual w o r l d . " The co-referential
proposition can be used by the system's reasoning processes to infer that
certain beliefs about the intension o f the Morning Star can be transferred to
(and from) the intension of the Evening Star. This will be discussed further
below.
Order Dependency
The set of nodes existing in a network will depend not only on what information is presented to the network but also on the order o f presentation. We
shall call this property order dependency. Consider Russell's (1906) example, "George IV wished to know whether Scott was the author of Waverly"
(p. 108). This apparently came about because, even though Scott was well
known at the time, Waverly was published anonymously. George the IV had
an intension for Scott and an intension for the author of Waverly but did
not know whether they were extensionally equivalent. A semantic network
simulating George IV, or just recording this fact, would need a different
node for each of these intensions. But what does this imply for how we
should represent the information that Scott wrote Ivanhoe (assuming that
the sentence "Scott wrote lvanhoe" is our first introduction to the novel)?
Must we represent this as two propositions, one for asserting the co-referentiality o f the intension for Scott and the intension for the author of
lvanhoe, and another for asserting that the author o f lvanhoe wrote Ivanhoe. Our answer is that the cognitive system creates intensions only as
needed for storing information about them. A separate concept was needed
for the intension of the author of Waverly only because there was thought
of that author before an identification was made with any previous intension. Psychological evidence for this analysis has been provided by the work
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o f Anderson and Hastie (1974), Anderson (1977, 1978), and McNabb
(1977). This will be discussed in a later section.
This theory would predict that a sentence such as " G e o r g e IV thought
that the author o f Waverlywas older than Scott," which requires two intensions having the same extension, would be harder to understand by someone
whose first introduction to the intension of the author of Waverly was via
the statement, "Scott wrote Waverly" than by someone who had already
thought about Scott and the author o f Waverly independently. The second
person would already have two intensions to use. The first person would at
first access the same intension for both Scott and the author o f Waverly, but
would then create at least one new concept for the intension o f the author o f
Waverly. We call this process splitting and will return to a more detailed
description of it later. This phenomenon would explain part o f the cuteness
o f the example "Shakespeare's plays weren't written by him, but by someone else of the same n a m e " (Hofstadter, Clossman, & Meredith, 1980).
Opacity as the Norm
A system that conforms to the Uniqueness Principle does not need the substitutivity of equals for equals as a basic reasoning rule, because no two
distinct nodes are equal. Co-referentiality between two nodes must be
asserted by a proposition. It requires inference rules to propogate assertions
from one node to another node which is co-referential with it. Thus, intensional representation implies that referential opacity is the norm and transparency must be explicity sanctioned by an inference process, unless nodes
are " m e r g e d . " Merging will be discussed in a later section.
Connections with Reality
The main objection to exclusive intensional representation seems to be that
if nodes represent only intensions, how could any alleged understanding
system so based have any connections with the outside world? To consider
this question, we must endow our modeled cognitive agent with sense and
effector organs. We will look at a robot system with sight and manipulators.
The robot needs a perceptual system in which some node, set of features, and so forth is triggered consistently when a given object is seen. If it
is to communicate reasonably with people about perceptual topics, it must
be able to make approximately the same perceptual distinctions that we
make. These perceptual nodes need not extensionally represent the objects
that trigger them. The perceptual nodes can be connected to the semanticconceptual nodes. This allows the robot to " r e c o g n i z e " objects, although it
could be fooled.
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The robot also needs effector organs that operate the manipulators
consistently, and connections between some semantic-conceptual nodes and
the effector organs so that it can operate its manipulators in a manner dictated by its reasoning (decide what to do).
Sensors and effectors, by supplying a connection between some node
in the semantic network and some object(s) in the actual world, finally provide referents for the node in one particular world. However, these referents
are only exemplars of the concept represented by the node. The significance
of the node remains its intension.
The Meaning of the Nodes
There are a number of formalisms compatible with the definition of propositional semantic network presented at the beginning of this paper. The formalism used here contains only propositions and individual concepts. We
will not specify a formal semantics for the network structures because the
meaning units of the network, the nodes, violate Frege's Principle of Compositionality (cf. Dowty, Wall, & Peters, 1981; p. 42). If a formal language
obeys the principle of compositionality, then for any non-atomic expression
in the language, there is a set of rules which enable one to determine the expression's meaning from the meaning of the expression's subexpressions. In
turn, the meaning of the subexpressions can be determined on the basis of
the meaning of the sub-subexpressions, and so on, recursively.
There are two properties of a formal semantic system that must hold
before one can even think of writing the above mentioned rules. The networks which appear in this paper have neither of those properties. First, in
order for the above mentioned recursion to terminate, the language must
have atomic expressions, or semantic primitives. However, the only primitives used in the networks are arc labels, which are non-conceputal, serve a
syntactic function, and have no meaning. Second, in order for the principle
of compositionality to apply at all, the meaning of an expression must not
change when it is embedded in another expression. The meaningful expressions in our network, the nodes, get their meaning from the expressions they
are embedded in (in addition to getting meaning from their subexpressions)
and thereby change their meaning whenever they are embedded in a new
expression.
Although our formalism does not obey Frege's principle, its characteristics which violate the principle can be found in Quillian's (1968)
writings. Quillian, as Brachman (1979) has pointed out, is most known for
suggesting that semantic information be stored in a subclass-superclass
hierarchy so that properties could be inherited from superclass to subclass.
There is, however, a less well known aspect of his writing that is relevant to
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our discussion. The next two quotations, taken from Quillian (1968), seem
to argue for a data structure that violates the principle of compositionality
for the two reasons stated above. In the quotations, we will interpret the
term " w o r d c o n c e p t " to mean node. First, Quillian argued that there are no
primitives:
there are no word concepts as such that are "primitive." Everything is
simply defined in terms of some ordered configuration of other things in
memory. (p. 239)
Second, Quillian argues that the meaning of a node is determined by a
search process which begins with that node:
a word's full concept is defined in the memory model to be all the nodes
that can be reached by an exhaustive tracing process, originating at its
initial, patriarchal type node... (p. 238, italics in original)
This implies that, as additional structure is added to the network, it
changes the modeled cognitive agent's understanding of the concepts represented by every node connected to the added structure. Martin (1981) has
applied the term d e c o m p o s i t i o n a l to nodes whose meaning is dependent
upon what they are constituents of. Because of this extreme form of decompositionality, the network described here will be inclined to m e m o r y confusions precisely because of these decompositional meanings. The mechanics
o f these confusions will be described in a later section. Anderson (1978, p.
51, Figure 1) appears to use decompositional meanings. It is an empirical
question as to whether humans are inclined to make the above mentioned
confusions. It m a y be the case that we will have to augment the network
notation so that the meanings are more stable and c o n f o r m to the second
prerequisite for compositionality. Woods' (1975) arguments for the need to
distinguish between the definitional information associated with a node and
the assertional information associated with a node are relevant here.
THE REPRESENTATION CONSTRUCTS
Here we introduce the network notation used in this paper. It is not the only
network notation compatible with semantic networks but uses perhaps the
fewest constructs. The network will have two kinds of nodes which we will
call base nodes and proposition nodes. The proposition nodes represerit
propositions and the base nodes represent individual concepts. All arcs are
directional and are either ascending or descending, and come in pairs such
that one arc of a pair is descending and the other is ascending. In the
diagrams of this paper, only the descending arc o f a pair is shown but there
is always an ascending arc (corresponding to the inverse o f the descending
arc) which is not shown. A node is a base node if it has no descending arcs
emanating from it other than a L E X arc. Otherwise, a node is a proposition
node.
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The L E X Arc
The purpose o f the LEX arc is to form an access route f r o m an individual
concept to a word in a lexical memory. The L E X arc is a device used in this
paper only to simplify the presentation. One drawback of the L E X arc is
that its function is different than the function o f the other arc.s. This is
because the object which it points to is not an intension, but rather an entity
in lexical m e m o r y . Using the L E X arc to associate a name, say " J o h n " ,
with a concept, say the intension of John, does not give the network knowledge (in a conceptual sense) that J o h n ' s name is " J o h n , " and we cannot tell
the network that it has the wrong name for the person it thinks is named
" J o h n . " A more consistent way to do this would be to have an intension for
the word " J o h n " as well as for the person John, and then use a proposition
to assert that the intension for " J o h n " is the word for the intension John.
Any links to lexical m e m o r y would then emanate from the intension for
" J o h n " and not the intension for John. For the purposes of exposition we
are representing an approximate distinction between a concept and a word
denoting the concept but we would not be able to describe the process of acquiring word meanings with this scheme. So the current scheme is being
used only to m a k e the diagrams and presentation simplier.
The important things to know about the L E X arc are that: 1) it points
from a concept to a word, and 2) the node it emanates from is an individual
concept and not a proposition.
Other Descending Arcs
Other than the LEX arc, descending arcs always point to arguments o f
propositions and the nodes from which they descend represent propositions.
A proposition node which has no descending arcs coming into it is said to be
a non-dominated node and represents a proposition that is believed by the
system. It is also necessary to be able to attach erasable, nonconceptual,
assertion tags to proposition nodes which are dominated. The purpose of
these tags is to indicate that the system believes those propositions. If a
dominated proposition does not have a belief tag then the system has no
opinion about its truth. The belief set of the semantic network consists exactly of the nodes which are non-dominated or which are tagged as true by
an assertion tag.
Extensional Equivalence
There is a case flame, called the equivalence case frame, which is used to
represent extensional equivalence. This case frame is used to assert that two
distinct intensions have the same extension in the real world. It does not say
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MAIDA AND SHAPIRO
what the extension is but rather only that they have the same extension.
Thus " T h e Morning Star is the Evening Star" is represented in the simplified network structure of Figure 1 and can be paraphrased as " T h e conceptual object denoted by 'Morning Star' is extensionally equivalent to the
conceptual object denoted by 'Evening S t a r ' . " The reason the case frame
has a special status is that it will interact with propositions involving knowing and believing in ways that other propositions will not interact.
Figure 1. A representation (node M3) for the propositional information in the sentence "The
Morning Star is the Evening Star."
Knowing and Believing
We will also use two different know relations. One will be used for knowing
a fact as in the sentence " J o h n knows that he is taller than Bill." The other
will indicate familiarity with a concrete or abstract object as in knowing a
person or game, or as in the sentence " P a t knows Mike's phone n u m b e r . "
We will call the sense of knowing a fact " k n o w 1" and the sense of being acquainted with a thing " k n o w 2 " . We justify these relations on the basis of
the introspection that knowing an object is different than knowing a fact.
Similarly, we will use two different believe relations, called "believe 1" and
"believe 2," to correspond to the two different know relations.
As stated earlier a propositional semantic network models the belief
system of a cognitive agent, which we will call " t h e system." Whenever any
of the relations involving knowing or believing appear in the network, they
will represent beliefs about beliefs.
We shall treat knowl only as correct belief rather than justified, correct belief for the following reason. If a cognitive agent believes that someone knows a facts, then the agent believes: 1) that the someone believes the
fact; 2) the fact is true; and 3) that the someone believes the fact for the
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
305
right reasons (as far as the cognitive agent can tell). The third stipulation
about "right reasons" is necessary to rule out belief for the wrong reasons
such as superstition or guessing. For example, there is at least one person
who believes that white can force a win in chess, and there is at least one
person who believes that white cannot. Therefore we know there is a person
who has a correct opinion about whether white can force a win. Nonetheless,
no one currently knows whether white can force a win. Since we are not able
to specify what "believing for the right reasons" means, we will discuss
knowing only in the sense of correct belief.
McCARTHY'S TELEPHONE NUMBER PROBLEM
The Main Example
We now address ourselves to M c C a r t h y ' s telephone number problem. What
follows is our representation, and its rationale, for sentence sequence (8).
(8) Pat knows Mike's phone number; Ed dials Mike's phone number;
and, Tony correctly believes that Mike's phone number is the same
as Mary's phone number.
This sentence sequence illustrates the distinctions upon which McCarthy's
example focuses. On the basis of (8) the system should conclude that Ed dials
Mary's phone number, yet it should not conclude that Pat knows M a r y ' s
phone number. Furthermore, it should not conclude that Tony knows either
Mike's or M a r y ' s phone number; however, if the system is subsequently
told that Tony knows one o f the numbers in particular, it should conclude
that Tony also knows the other number. Figure 2 shows the network representation o f the information contained in (8). (Note: Although it does not
appear in the figure, assume M5 has been tagged as true by an assertion tag.)
Critical to our discussion is an explication of the system's understanding the concept of node M7 of that figure. Node M7 is:
Something which Pat knows, and
something which Ed dials, and
something which is Mike's phone number, and
something that is co-referential with Mary's phone number, and
something that Tony knows is co-referential with Mary's phone number.
In order to explicate the node's full concept, it was necessary to traverse the
entire network, and the network is the sum total of the system's beliefs.
The assertion that node M7 is co-referent with M a r y ' s phone number
is just as much a part its meaning as the assertion that it is Mike's phone
number. However, we do not want the system to decide that Pat knows
M a r y ' s phone number, so how do we avoid this? This is where extensional
equivalence links acquire their special status. If the system believes that
X
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X
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W
X
X
I&i
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Ma
X
IAI
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phone
number
Figure 2. A representation for the information in the sentence sequence: "Pat knows Mike's
phone number; Ed dials Mike's phone number; and, Tony correctly believes that Mike's
phone number is the some as Mary's phone number."
306
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
307
some agent knows some intensional concept, then it will assume that the
agent knows all o f the propositions asserted about the intensional concept
except those propositions which consist of the extensional equivalence case
frame (e.g., M5) or which contain the extensional equivalence case frame
(e.g,, M14). So the system will assume that Pat knows M4, M l l , and MI5.
Now the system could be mistaken; Pat need not necessarily know M15.
This performance characteristic would predict corresponding kinds o f
memory confusions in humans. Further discussion of this appears later in
the paper in the section titled "Merging and Splitting N o d e s . "
Further Examples
To further illustrate how we would use the representation, we will look at
two more sentences, and then return to the question of transparency verses
opacity. Consider (9) below.
(9) Mike has two phones. One is 831-1234. The other is 831-4321.
Figure 3 shows how we represent it. The next example illustrates how we
handle designators which fail to refer, as seen in (10) below.
(10) Mike doesn't have a phone.
There are two ways to represent this utterance. The first involves the intension of nothing (for a discussion of this intensional object see, Heath, 1967).
It is the notion of non-existence. The representation is depicted in Figure 4,
and if one o f the non-dominated nodes were submitted to a language generator (node M4 or M5), it might produce the sentence "Mike's phone number is non-existent." The other way employs universal quantification and,
as shown in Figure 5, asserts that for all x, x is not Mike's phone number.
The quantification arc is taken from the SNePS semantic network formalism (Shapiro, 1979a).
Transparent Relations Propogate by Inference
We now return to describing how the representation for McCarthy's telephone number problem can support processes which simulate referential
transpareocy and opacity. Opacity is the norm because for instance, in the
situation of sentence sequence (8), Mike's phone number and Mary's phone
number are distinct intensions which are extensionally equivalent; but extensional equivalence is not equality, so we do not encounter the problem o f
substitution of equals for equals. Transparency, however, requires some
sort o f inference process. What is needed is an inference or production rule
which propogates assertions across equivalence arcs, but which has an ante-
.~/
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,7
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Figure 3. The representation for Mike having two phones.
k
l;
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Figure 4. The representation for Mike not having a phone.
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Figure 5. Another representation for Mike not having a phone.
309
310
MAIDA AND SHAPIRO
cedent trigger pattern that matches only assertions involving transparent
operators. This entails that the system have the conceptual knowledge that
the relation dial is transparent but know is not. Such an inference rule
would then enable the system to add to its data base that Ed dials Mary's
phone number from the information given in (8); yet the system would not
add that Pat knows Mary's phone number, because know is not transparent
and would not satisfy the trigger pattern of the inference rule.
There are situations in which assertions involving opaque operators
can also propogate across equivalence paths. Tony in (8) knows that Mike's
phone number and Mary's phone number are extensionally equivalent, so
any assertion with Tony as the agent and Mike's phone number (node M7)
as the object, regardless of whether it involves an opaque operator, should
be able to propogate across that equivalence path. In short then, if a cognitive agent knows that two concepts are extensionally equivalent, then for
that agent all operators are transparent with respect to that path. The appendix contains examples of inference rules which propogate assertions
across an equivalence path. No claim is made that they are complete.
REPRESENTING TRUTH VALUE
This section makes several points. First, the concept of the truth value of
some proposition is intensionally distinct from its particular truth value
(true or false) and at times it is necessary to make this distinction explicit in
the representation. Second, the same information can be represented by two
different configurations of concepts. This illustrates what we mean by order
dependency. And third, we contrast the behavior of the system's beliefs
about believing with its beliefs about knowing (correct belief).
Figure 6 shows the representation for sentence (1 l), with the proviso
that the system has already wondered about the truth value of the proposition underlying the sentence "John is taller than Bill." An implication of
our discussion of order dependency is that a distinct intension for the truth
value of a proposition will be created only if the system wonders about the
truth value of that proposition before actually learning its truth value.
(ll) It is true that John is taller than Bill.
This treatment embodies the claim that the extension of a proposition is its
truth value. Node M8 is the intension for the truth value of the proposition
underlying the sentence "John is taller than Bill." Node M6 represents the
individual concept of truth. When John wonders whether he is taller than
Bill as in sentence (5), he is trying to determine the co-reference of node M8.
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
14,1
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Figure 6. The r e p r e s e n t a t i o n f o r the propositional i n f o r m a t i o n contained in the sentence "It
is true that John is t a l l e r than Bill."
If Tony believes, as in sentence (1), John knows whether John is taller than
Bill, then Tony believes John's description of node M8 is complete even
though Tony's is not necessarily complete.
We emphasize that the configuration of nodes used to represent (11)
depends on the order in which the system thinks of them. If someone is
directly told that John is taller than Bill and does not have to wonder about
it, then the representation would be much simpler, as shown in Figure 7, in
which node M4 represents the proposition underlying the sentence " J o h n is
taller than Bill."
Since (11) is an extraposed version of the sentence "That John is taller
than Bill is true," we suspect it carries the presupposition that the listener
has in fact wondered about the truth value of the embedded proposition,
and so the representation depicted in Figure 6 is the correct one for this sentence. The EQUIV-EQUIV case frame indicates that two intensions already
represented in the network are extensionally equivalent in the actual world.
Node M6 of Figure 6 would presumably already exist in anyone's memory
who has some notion of truth. Mode M8 would exist in people's memory
who have wondered about the truth value of "John is taller than Bill"
before learning its actual truth value.
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MAIDA AND SHAPIRO
,.I
Figure 7. The representation (node M4) for the propositional information contained in the
sentence "John is taller than Bill."
The reader might entertain the possibility of using the above technique
as a general method o f asserting propositions in the network. This is not
possible because it would lead to an infinite regress of assertion embeddings.
If the EQUIV-EQUIV case frame were necessary to assert a proposition
then Figure 6 would not assert utterance (11) because node M7 has not been
asserted by the EQUIV-EQUIV case frame. The convention of taking toplevel nodes as being asserted alleviates this problem.
In order to represent sentence (3), duplicated below, we use "believe
2 . " As already mentioned, it means to be familiar
(3) John holds an opinion about whether he is taller than Bill.
(4) John believes he is taller than Bill or John believes he is not taller
than Bill.
with, or apprehend, some intension. Figures 8 and 9 contrast our representations o f sentences (3) and (4). In Figure 9, sentence (4) is represented by
node M8 which is a proposition involving exclusive-or. A feature inherent in
the use of " k n o w 2 " is that the task of appraising in exactly what manner
the agent of the " k n o w 2 " relation is familiar with, or apprehends, an individual concept requires the use o f inference rules. " K n o w 2 " says nothing
in itself except that the agent is familiar in some domain specific way with
the individual concept that is the object of the relation. There must also be a
INTENSIONAL CONCEPT
IN SEMANTIC NETWORKS
313
believeZ
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Figure 8. The representation (node M8) for the propositional information contained in the
sentence "John holds an opinion about whether he is taller than Bill."
way for the specific facts that an agent knows about the concept to be independently asserted. An illustration of this point is depicted in Figures 10 and
11. Node M8 in Figure 10 does not directly represent
(12) John knows that he is taller than Bill.
sentence (12), but rather entails sentence (12). Node M5 in Figure 11 does
directly represent (12). Believing that P and having a correct opinion about
:314
MAIDA AND SHAPIRO
believe1
REL
RE L
f...~,
ARG2
X
Ell
r
taller
Figure 9. The representation (node M8) for the propositional information contained in the
sentence "John believes he is taller than Bill or John believes he is not taller than Bill."
whether P are two different intensions and therefore should be represented
by two distinct nodes. The network structure of Figure 10 does not explicitly
assert what John's opinion actually is. Using the inference rule (13) below,
the information in Figure 11 could be deduced from the information in
Figure 10.
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
315
(13) If the system believesl that some cognitive agent knows2 whether
some proposition P and the system believesl that P, then the system can conclude that the agent believesl that P.
The following example illustrates the behavior of this kind of system.
Suppose you were a college freshman majoring in computer science, and suppose you believed (incorrectly) that pi was a rational number. Naturally, you
would also believe that your computer science professor also knew whether pi
was rational. By applying the above inference rule, you would erroneously,
but properly, conclude that your professor believed that pi was rational.
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Figure 10. The representation for the s e n t e n c e s e q u e n c e : "John holds a correct opinion
about whether he is taller than Bill; it is true that John is taller than Bill."
316
MAIDA AND SHAPIRO
know1
MI
Figure 11. The representation (node M5) for the propositional information contained in the
sentence "John holds a correct opinion that he is taller than Bill."
R E P R E S E N T I N G YES-NO QUESTIONS
In order to support the entire range o f discourse processing it is necessary
for a knowledge representation in general, and a semantic network in particular, to have the ability to represent questions. Although it is possible for
a network which does not represent questions to interface with a processor
that enables it to answer questions (e.g., an ATN parser-generator; Shapiro,
1979b), the network itself would intrinsically not have the ability to remember which question were asked. The need to represent questions is illustrated
by sentences o f the sort "Since John asked me whether he was taller than
Bill, I assumed he had never met Bill." In order to represent this sentence, it
is first necessary to represent the question embedded within the subordinate
clause.
We now turn to the problem of representing a yes-no question in a
propositional semantic network. A question is not an individual concept,
nor is it a proposition, but it must be represented in a propositional network
by some configuration of individual concepts and propositions. It is not the
case that a question can be paraphrased into a propositional form. Consider
the line of dialog below (14) and the attempt to propositionalize it (15).
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
317
(14) Mary said, "John are you taller than Bill?"
(15) Mary asked John whether he was taller than Bill.
The paraphrased form superficially resembles a proposition except for a
constituent centered around " w h e t h e r , " which cannot be propositionalized.
There is a way to circumvent the obstacle by noticing that the sentence
resembles sentence (5). We can generate (16) from (15) by replacing " a s k "
with " w o n d e r " as shown below.
(16) Mary wondered whether John was taller than Bill.
Our treatment of " w o n d e r " described earlier applies here and can be extended to " a s k . " Sentence (15) is an enquiry about the truth value of the
proposition underlying the sentence " J o h n is taller than Bill." The literal
interpretation of all yes-no questions can be handled in this manner. Our
representation of (15) is shown in Figure 12. The important thing to note is
that the representation captures the fact that the question is an enquiry about
the reference o f the truth value of a proposition. The ability to represent
this concept supplies the groundwork to build processes (e.g., programs,
production rules, inference rules) in the system which uses this concept. The
representation can trigger inference rules which will ensure that the system
appropriately understands word senses like " a s k . " " A s k " means something like "enquire into the identity o f . "
The indirect speech act literature contains many examples o f questions
such as, " C a n you pass the salt?" which are not interpreted in natural discourse as questions. Rather they effect the listener as if he had heard some
other illocutionary act; in this case it is a request. However, humans are able
to understand that, literally, this sentence is a yes-no question and it follows
that they must be able to represent this literal interpretation. Furthermore,
most accounts of indirect speech acts build on the assumption that the propositional content of the speech act has been extracted. Hence, we would like
to represent this literalness in our network.
We will discuss wh-questions in the section after next section, after we
discuss the process of node splitting.
M E R G I N G AND S P L I T T I N G NODES
Merging Nodes
Many writers point out the need for merging nodes which refer to the same
physical object (e.g., Anderson, 1977, 1978; Hofstadter, Clossman, &
Meredith, 1980). This kind o f process seems attractive because it would
serve to reduce " c l u t t e r " and simplify the crossreferencing problems between information in memory. C o m m o n sense seems to dictate that a system
which maintains multiple nodes that are known to be co-referential is inefficieht. This view is expressed by Hofstadter et al.:
318
MAIDA AND SHAPIRO
ARG3
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Figure 12. The representation (node M9) for the propositional information contained in the
sentence "Mary asks John whether he is taller than Bill."
It is inevitable in any representational formalism that distinct nodes will
sometimes be manufactured that, it turns out later, stand for the same
thing . . . . What happens when one finally finds out that the two nodes
represent the same thing? Clearly, they have to be fused somehow into
one new node. (p. 4)
It is true that this kind o f heuristic leads to increased ability to perform inferences in transparent contexts, however it has the disadvantage o f not
being able to inhibit spurious inference processes in domains involving
opaque contexts. For instance, as already pointed out, if a system has two
separate nodes for Mary's phone number and Mike's phone number, along
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
319
with an assertion that they are extensionally equivalent, then it is not difficult to inhibit the system from concluding that John knows Mike's phone
number if it is told that John knows Mary's phone number. But if a merge
or copy process were to operate on the two nodes known to be extensionally
equivalent, as Hofstadter et al., and Anderson propose, so that all o f the information separately associated with each o f the nodes is merged onto one
node, then the spurious inference in the above example would be difficult to
inhibit if the system were still going to make transparent inferences. Thus
the process of merging nodes must not always take place.
Constraints on Merging Nodes
One possibility for policing this process is to set the constraint that a maximum of one predicate (assertions about co-reference are exempt) can be
asserted per node. This amounts to a total suppression o f any process which
merges nodes; and, although it guarantees a representation with sufficient
resolution to appropriately trigger both opaque and transparent inference
processes, it creates a maximally inefficient system for cross referencing
properties among extensionally equivalent concepts in transparent contexts.
This option seems drastic and cumbersome, and we concur with Anderson
and Hofstadter et al., in that it does not agree with our intuition either.
Furthermore, there is experimental evidence that some merging of nodes
does take place in humans. Anderson (1977), in addition to demonstrating
that a subject can have two distinct nodes which are extensionally equivalent, has obtained evidence that subjects are strongly biased against maintaining two such distinct nodes if they know that the nodes are extensionally
equivalent. Usually in such situations one of the two nodes is less strongly
memorized than the other node. What subjects are inclined to do during the
course of use is to place duplicate copies of the information which reside at
the less established node to the more established node and then gradually
abandon use o f the less established node.
However, back in McCarthy's telephone number problem, the nodes
for Mary's phone number and Mike's phone number cannot be merged. The
nodes exist in an opaque context. In all o f Anderson's experiments, his stimulus materials were instances o f transparent reference. As we said earlier, in
transparent contexts, merging o f nodes leads to optimal performance.
Let us look at Anderson's (1978) stimulus materials. Subjects were
asked to memorize the following kinds of sentences:
(17)
(18)
(19)
(20)
(21)
The
The
The
The
The
smart Russian is the tall lawyer.
smart Russian cursed the salesgirl.
smart Russian rescued the kitten.
tall lawyer adopted the child.
tall lawyer caused the accident.
320
MAIDA AND SHAPIRO
These materials contain no opaque operators. However, we can prefix
each o f these study sentences with the phrase " J o h n believes t h a t " ; then if a
subject memorizes these modified study sentences, he or she will generate
the same subconfiguration of nodes in memory as before but this time
within an opaque context. If a subject fully processes the semantics o f the
word "believe" (unfortunately, tuning the task demands to force the subject to fully process "believe" might not be so easy) then during the experiment, he or she must process the nodes in a way that maintains the separate
intensions. Specifically, the trend in the reaction time data which was
observed that indicated subjects were copying information from one coreferent node to another should be absent.
We suggest that the process of merging nodes is inhibited when an
opaque context is created but not otherwise. This creates a compromise
system which will process instances o f transparent reference efficiently yet
process instances of opaque reference accurately.
Confusions
We as yet have not succeeded in devising a representation which does not
make any semantic confusions. The problem can be seen by examining
Figure 2. After the system is told the information in sentence sequence (8), it
will answer " y e s " to the question "Does Pat know Ed dials Mike's phone
n u m b e r ? " The reason is that any straight-forward algorithm that adds the
assertion to the data base that Pat knows M4 will also cause it to add to the
data base that Pat knows M15 because both nodes have the same status in
the network. Humans are certainly able to avoid making this mistake, but
the representation can be patched up, either by augmenting the processes
which use the representation or by augmenting the representation itself.
Without changing the representation, the only way to inhibit adding
the fact that Pat knows node M15 while still allowing the inference that Pat
knows node M4 is by using highly domain specific inference rules. Perhaps
humans can generate these hypothesized rules quite quickly. It seems that
this approach however would lead to a system whose performance was likely
to degrade very time it learned something new because there would be the
possibility of a new confusion. With each new confusion, a new domain
specific inference rule would have to be created to inhibit the confusion.
This is reminiscent of an EPAM-like theory of forgetting.
The networks used in this paper use only assertional information. Instead of adding domain specific inference rules, we could augment the
representation to include structural, or definitional, information, and then
change the semantics of the network so that the meaning o f a node was only
what the structural information said what it was. NotationaUy this could be
done by adding functional individuals to the present representation con-
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
321
structs (cf. Maida, 1982). The purpose of definitional information would be
to define intensions. Although Woods (1975, p. 58) argued for the need to
distinguish between structural and assertional information, psychologists
have not as yet been inclined to make such a distinction and tend to accept
Quillian's formulation (cf. Collins & Loftus, 1975) o f a node's full concept
as adequate. Anderson (1976, p. 243) does use structural information to
represent transparent versus opaque reference but he does not refer to the
distinction in his experimental work (e.g., Anderson, 1978).
SpliCing
Consider the following situation. What if a memory node created in a transparent context and with several descriptions fused or merged onto it, gets
puts into an opaque context? Returning to the phone number problem,
what if a cognitive agent learns that Mike and Mary have the same phone
number as a consequence of learning that they live together? Then the two
descriptions would be attached to the same node as shown in Figure 13.
Now suppose this cognitive agent hears sentence (22).
(22) Pete doesn't know that Mike's phone number is the same as Mary's
phone number.
The network structure depicted in Figure 13 could not become part of the
representation structure for sentence (22) because that structure treats the
concepts of Mike's and Mary's phone numbers as being the same, rather
than being extensionaUy equivalent. Our cognitive agent must make a new
)
)
Figure 13. The representation for Mike's and Mary's phone number being the same if there
is no immediate need to treat them as separate intensions.
322
MAIDA AND SHAPIRO
distinction before he can comprehend (22). It seems necessary that two
nodes be constructed to separately represent Mike's phone number and
Mary's phone number, and they must be made extensionally equivalent to
the original node. We call this process splitting and it was mentioned earlier
in our discussion of Scott writing Waverly. The final representaiton is
shown in Figure 14 in which node M16 represents the proposition of (22).
This analysis predicts that a person who learns about Mike's and Mary's
phone number in a transparent context will have more difficulty subsequently comprehending (22) than a person who learns this same information in an opaque context because a split must take place.
Because of the probable computational overhead involved in splitting
nodes, perhaps this kind of strategy might only be utilized when the system
is operating in "careful n o d e , " as in social situations where misunderstandings could be embarrassing or costly. Also from a cognitive developmental
perspective, this operation should occur late in the developmental sequence.
And perhaps the usual mode o f human functioning leads to treating opaque
operators as transparent. Witness the difficulty a teacher has in trying to
understand why a student does not understand. If the teacher was facile at
processing opaque contexts, he or she would be able to accurately assess the
student's knowledge state.
In light o f the optional nature o f processing associated with opacity,
some unanswered experimental questions are raised? What are the factors
which trigger opaque processing in humans? Developmentally, when does
the ability for opaque processing appear in children? For instance, suppose
that a person knows that Jim's wife is Sally's mother and is then told that
Mike wants to meet Jim's wife (adapted from Creary, 1979). Under what
circumstances might the person assume that Mike realizes he would like to
meet Sally's mother and under what circumstances might that person feel
the need to determine whether Mike knows Jim's wife is Sally's mother.
Consider the following two sentences taken from Anderson (1978).
Anderson points out that the former sentence is an instance of
(23) I am looking for the best lawyer in town.
(24) I am looking for my little old mother.
opaque reference and the latter is an instance of transparent reference.
Given that the difference in interpretation is probably not attributable to
their very slight differing syntactic structure, what is determining whether
the interpretation is transparent or opaque? The type of interpretation
seems to depend on inference processes taking place in the listener which actively assess the knowledge state of the speaker. To illustrate, consider the
interpretation of sentence (25) below, depending on whether a foster child,
or an earthquake survivor is speaking.
(25) I am looking for my lost mother.
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324
MAIDA AND SHAPIRO
In the case of the foster child, the listener realizes that the child has probably
never known its mother. Whereas in the case of the earthquake survivor, the
listener knows that the survivor has someone specific in mind.
REPRESENTING WH-QUESTIONS
The treatment of wh-questions becomes clearer when one recognizes the
opacity of the complement position of ask. The meaning of sentence (26) is
changed if we substitute the phase "Mary's phone number" in place of
"Mike's phone number" even if Mike and Mary have the same phone
number.
(26) Pat asks Joe for Mike's phone number.
Therefore, in order to represent (26), we must create a new node which
represents the intension of the Mike's phone number which Pat asks Joe
for. We then equivalence it to the existing node. The resulting interpretation
is depicted in Figure 15.
There are additional constraints to consider. We do not want to create
a split to answer a simple question if we have already postulated splitting to
be computationally expensive; and we want to use as much shared network
structure as possible. The representation is constructed and integrated into
the rest of memory as follows. The relation ask has three arguments: 1) the
person doing the asking; 2) the person asked; and, 3) the thing being asked
about. Only the thing being asked about is treated opaquely, so it is the only
node that does not get matched to the network as the question is being
parsed. Rather, it must be asserted to be extensionally equivalent to some
other node in memory. Referring to Figure 15, node M8 gets matched to
memory via the network pattern determined by nodes M9, M2, and M1.
The node which is found as a result of this pattern match (M7 in this case)
will be asserted to be extensionally equivalent to node MS. The system
should be able to use information which is asserted about M7 to answer the
question. In summary then, the listener constructs a representation of the
question, matches it to the rest of the network, and finds a node which plays
two roles: 1) it is treated as being extensionally equivalent to the concept
being asked about; and, 2) it should serve as the access route to information
suitable for answering the question. Note also that the system remembers
who asked whom what question.
The question is, in fact, an enquiry about a particular intension, and
that is the feature the representation unambiguously captures. But it is not
so clear for the system as to how to determine what constitutes a good
answer to the enquiry about the intension. This sort of task requires domain
specific knowledge. It seems necessary to include discourse rules in the
)<
MI
IM
JJ
,.I
other
info
X
lU
._1
number
REL
Figure 15. The representation (node MIO) for the propositional information contained in the
sentence "Pat asks Joe for Mike's phone number."
325
326
MAIDA AND SHAPIRO
system to decide exactly what information the questioner is looking for. It is
a mysterious phenomenon that humans perceive wh-questions as asking for
specific information; on a literal level, they are vague, (e.g., Where is the
salt? In the salt shaker). One possible rule for answering questions about
phone numbers is given below in (27).
(27) If a person asks you for a description of a phone number that you
believe2 or know2, then he wants you to generate a linguistic description of a digit sequence that is extensionally equivalent to the
phone number.
Lehnert (1978), Allen (1979), and Allen and Perrault (1980) have extensively
treated the problem o f deciding what is so specific about specific questions
in natural language discourse.
A more general rule for answering wh-questions, probably reserved
for use when the system cannot find relevant domain specific knowledge, is
given below in (28).
(28) When answering a wh-question, use any identifying description of
the entity that the questioner asked about, but which the questioner himself did not use in formulating the question.
Thus if Joe answered (26) by saying, " O h , Mike's phone n u m b e r " then rule
(28) would be violated. Alternatively, if he said " O h , that's Mary's phone
n u m b e r , " then rule (28) would be satisfied but not rule (27).
CONCLUSION
This paper makes an integrated statement concerning the semantic status of
nodes in a propositional semantic network, claiming that nodes in such a
network represent only intensions. Within the network, the only reference
to extensionality should be via some mechanism to assert that two intensions have the same extension (e.g., The Morning Star is the Evening Star).
We have also shown how processes which simulate referential transparency
or referential opacity can operate on the network. Our analyses have been
influenced by analytic philosophy, artificial intelligence, and cognitive
psychology.
We have employed this framework in three application areas to illustrate the nature o f its solutions. First, we map out a solution to McCarthy's
telephone number problem, which he devised to succinctly capture the difference between referential transparency and opacity. Second, we directly
represent the notion o f the truth value of a proposition as is needed to represent a sentence like " J o h n knows whether he is taller than Bill." Finally, we
represent sentences like "Since John asked me whether I was taller than
Bill, I assumed he never met Bill."
INTENSIONAL CONCEPTS IN SEMANTIC NETWORKS
327
We also discuss some of the psychological implications of network
processes which we call node merging and node splitting. It has been well
recognized that a merge process should occur for co-referential nodes but
little attention has been given to restrictions on this merge process and to the
need for a splitting process. We theorize that merging should be inhibited in
opaque contexts and suggest that Anderson's results on node merging will
not generalize to opaque contexts. We also point out the need for a splitting
process.
The formalism we use in this paper employs only assertional information and no structural, or definitional, information. This is consistent with
network models in the psychological literature. In particular, neither Anderson (1978), nor Collins and Loftus (1975) mention the distinction. Our networks our prone to memory confusions to which the psychologically based
networks will also be vulnerable. The notation employed in this paper can
be augmented, by the use of functional individuals (cf. Maida, 1982) to
eliminate the tendency for memory confusions. Whether psychologists
should employ the use of functional individuals is an empirical question.
This change in formalism, however, results in a drastic change in the semantic interpretation of network structure, as Quillian proposed it.
Propositional semantic networks continueto be a fruitful data structure by which to model the organization of the human mind.
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APPENDIX
This a p p e n d i x c o n t a i n s a list o f inference rules whose p u r p o s e is to p r o p o g a t e assertions across extensional equivalence paths. This is not a c o m p l e t e list to e n a b l e all
valid inferences, a n d the specific f o r m a t o f these rules would d e p e n d o n the specific
n o t a t i o n o n e used. T h e rules consist o f c o n d i t i o n - a c t i o n pairs in which the c o n d i t i o n
specifies a p a t t e r n t h a t must m a t c h the n e t w o r k in o r d e r for the rule to apply a n d the
action builds m o r e n e t w o r k structure. T h e c o n d i t i o n o f a rule consists o f a sequence
o f clauses which all must m a t c h the n e t w o r k . Clauses specify n e t w o r k structure as
follows:
(lst-arg-slot relation-slot 2nd-arg slot)
or,
(property-slot arg-slot)
or,
(arg-slot equivalent arg-slot)
Variables are prefixed with a q u e s t i o n m a r k a n d while u n b o u n d will m a t c h a n y n o d e
in the n e t w o r k p r o v i d e d the rest o f the clause m a t c h e s t h a t part o f the n e t w o r k . O n c e
a variable matches a node, it is b o u n d to t h a t n o d e for t h e rest o f the application o f
that rule.
330
MAIDA AND SHAPIRO
Rule 1:
(is-transparent ?rel) &
(?agent ?rel ?objl) &
(?objl equivalent ?obj2) = = >
(?agent ?rel ?obj2)
Note: For example,
If likes is a transparent relation and
John likes Mary and
Mary is Sally's mother then
John likes Sally's mother.
However, he may not believe he likes Sally's mother.
Rule 2:
(?agent believe (?agent ?rel ? o b j l ) ) &
(?agent believe (?objl equivalent ?obj2))
- - > (?agent believe (?agent ?rel ?obj2))
If a person believes Jim's wife is Sally's mother and he believes he wants to
meet Jim's wife, then he believes he wants to meet Sally's mother regardless of
whether Jim's wife in fact is Sally's mother.
Rule 3:
(?agent know (?agent ?rel ? o b j l ) ) &
(?agent believe (?objl equivalent ?obj2))
- - > (?agent believe (?agent ?rel ?obj2))
Note: For example,
If John knows he likes Mary and
John believes that Mary is Sally's mother
then he believes he likes Sally's mother.
Although the premises of this rule are stronger than those of rule 2, the conclusion is the same as rule 2.
Rule 4:
(?agent know (?agent ?rel ? o b j l ) ) &
(?agent know (?objl equivalent ?obj2))
- > (?agent know (?agent ?rel ? o b j l ) )
-
The conclusion of this rule is stronger than that of rule 3 because the system
believes the agent is correct in his belief about the coreferentiality of objects 1 and 2.